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Volume 27, Issue 4
Global Existence and Asymptotic Behavior for a Coupled System of Viscoelastic Wave Equations with a Delay Term

Mohamed Ferhat & Ali Hakem

DOI: 10.4208/jpde.v27.n4.2

J. Part. Diff. Eq., 27 (2014), pp. 293-317.

Published online: 2014-12

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  • Abstract
We are interested in the study of a coupled systemof viscoelasticwave equations with a delay term. Firstly global existence of the solutions is proved. The asymptotic behavior is obtained by using multiplier technique proved by A. Guessmia [1], however in the unstable set for certain initial data bolstered with some conditions, we obtain the blow up of the solutions for various sign of initial energy negative, positive or null. We use the same technique in [2] with a necessary modification imposed by our problem. This improves the earlier results in the literature.
  • Keywords

Global existence energy decay nonlinear damping

  • AMS Subject Headings

35L05, 35L15, 35L70, 93D15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

ferhat22@hotmail.fr (Mohamed Ferhat)

hakemali@yahoo.com (Ali Hakem)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-27-293, author = {Ferhat , Mohamed and Hakem , Ali}, title = {Global Existence and Asymptotic Behavior for a Coupled System of Viscoelastic Wave Equations with a Delay Term}, journal = {Journal of Partial Differential Equations}, year = {2014}, volume = {27}, number = {4}, pages = {293--317}, abstract = { We are interested in the study of a coupled systemof viscoelasticwave equations with a delay term. Firstly global existence of the solutions is proved. The asymptotic behavior is obtained by using multiplier technique proved by A. Guessmia [1], however in the unstable set for certain initial data bolstered with some conditions, we obtain the blow up of the solutions for various sign of initial energy negative, positive or null. We use the same technique in [2] with a necessary modification imposed by our problem. This improves the earlier results in the literature.}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v27.n4.2}, url = {http://global-sci.org/intro/article_detail/jpde/5144.html} }
TY - JOUR T1 - Global Existence and Asymptotic Behavior for a Coupled System of Viscoelastic Wave Equations with a Delay Term AU - Ferhat , Mohamed AU - Hakem , Ali JO - Journal of Partial Differential Equations VL - 4 SP - 293 EP - 317 PY - 2014 DA - 2014/12 SN - 27 DO - http://doi.org/10.4208/jpde.v27.n4.2 UR - https://global-sci.org/intro/article_detail/jpde/5144.html KW - Global existence KW - energy decay KW - nonlinear damping AB - We are interested in the study of a coupled systemof viscoelasticwave equations with a delay term. Firstly global existence of the solutions is proved. The asymptotic behavior is obtained by using multiplier technique proved by A. Guessmia [1], however in the unstable set for certain initial data bolstered with some conditions, we obtain the blow up of the solutions for various sign of initial energy negative, positive or null. We use the same technique in [2] with a necessary modification imposed by our problem. This improves the earlier results in the literature.
Ferhat , Mohamed and Hakem , Ali. (2014). Global Existence and Asymptotic Behavior for a Coupled System of Viscoelastic Wave Equations with a Delay Term. Journal of Partial Differential Equations. 27 (4). 293-317. doi:10.4208/jpde.v27.n4.2
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